New infinite hierarchies of polynomial identities related to the Capparelli partition theorems
Abstract
We prove a new polynomial refinement of the Capparelli's identities. Using a special case of Bailey's lemma we prove many infinite families of sum-product identities that root from our finite analogues of Capparelli's identities. We also discuss the q 1/q duality transformation of the base identities and some related partition theoretic relations.
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